Application of group theory to quantum information and quantum computation

The method of group theory leads to the very simple and elegant description of the synthesis of quantum information and quantum computation processes. For example reversible quantum logic gates can be analyzed by using group theory. It is known that quantum entanglement can be also formulated by using group theory. The algorithms for quantum computations can be constructed in the framework of hidden subgroup. The Quantum Fourier Transform which can be used to solve some logarithm problems also closely related to the hidden subgroup and finite groups. There is also an interesting link between SU(2) symmetry and quantum beam splitter transformation, as well as n-qudit systems and quantum codes. We also found some fingerprints of quantum entanglements- in exceptional groups such as E6, E7 and E8- generating by Quantum Gates and that concisely related with Clifford Groups, Coxeter Groups. During realization of Quantum Gates it is very important establishing connection between Coxeter Groups and qubit symmetries ( e.g. unitary transformation). We would like to mention here that formalism of quantum information and quantum computation lies in the clever use of group theory. We also point out that quantum information and quantum computation theory are young sciences but they are very fast moving and very popular because of their fascinating beauty. Consequently, all this group theoretical analysis would be worth to solve the complicated problems in quantum information and computation theory.